Kepler

PROGRESS

SO

KEPLER

W. Wt BRYANT

KEPLER

PIONEERS OF PROGRESS

MEN OF SCIENCE

EDITED BY S. CHAPMAN, M.A., D.Sc., F.R.S.

KEPLER

BY

WALTER W. BRYANT

OF THE ROYAL OBSERVATORY, GREENWICH

LONDON :

SOCIETY FOR PROMOTING
CHRISTIAN KNOWLEDGE

NEW YORK; THE MACMILLAN COMPANY
1920

CONTENTS.

CHAP. PAGE

I. ASTRONOMY BEFORE KEPLER 5

II. EARLY LIFE OF KEPLER ........ 13

III. TYCHO BRAKE 19

IV. KEPLER JOINS TYCHO 28

V. KEPLER'S LAWS 35

VI. CLOSING YEARS 52

APPENDIX I. — LIST OF DATES 59

APPENDIX II. — BIBLIOGRAPHY 60

GLOSSARY 61

494580

CHAPTER I.

ASTRONOMY BEFORE KEPLER.

IN order to emphasise the importance of the reforms
introduced into astronomy by Kepler, it will be well to
sketch briefly the history of the theories which he had
to overthrow. In very early times it must have been
realised that the sun and moon were continually changing
their places among the stars. The day, the month, and
the year were obvious divisions of time, and longer
periods were suggested by the tabulation of eclipses.
We can imagine the respect accorded to the Chaldaean
sages who first discovered that eclipses could be pre-
dicted, and how the philosophers of Mesopotamia must
have sought eagerly for evidence of fresh periodic laws.
Certain of the stars, which appeared to wander, and were
hence called planets, provided an extended field for these
speculations. Among the Chaldaeans and Babylonians
the knowledge gradually acquired was probably confined
to the priests and utilised mainly for astrological pre-
diction or the fixing of religious observances. Such
speculations as were current among them, and also
among the Egyptians and others who came to share
their knowledge, were almost entirely devoted to myth-
ology, assigning fanciful terrestrial origins to constel-
lations, with occasional controversies as to how the earth
is supported in space. The Greeks, too, had an elaborate
mythology largely adapted from their neighbours, but
they were not satisfied with this, and made persistent

(5)

6 .; :: : A KEPLER

attempts to reduce the apparent motions of celestial
objects to geometrical laws. Some of the Pythagoreans,
if not Pythagoras himself, held that the earth is a sphere,
and that the apparent daily revolution of the sun and
stars is really due to a motion of the earth, though at
first this motion of the earth was not supposed to be one
of rotation about an axis. These notions, and also that
the planets on the whole move round from west to east
with reference to the stars, were made known to a larger
circle through the writings of Plato. To Plato moreover
is attributed the challenge to astronomers to represent
all the motions of the heavenly bodies by uniformly
described circles, a challenge generally held responsible
for a vast amount of wasted effort, and the postponement,
for many centuries, of real progress. Eudoxus of
Cnidus, endeavouring to account for the fact that the
planets, during every apparent revolution round the earth,
come to rest twice, and in the shorter interval between
these " stationary points," move in the opposite direction,
found that he could represent the phenomena fairly well
by a system of concentric spheres, each rotating with
its own velocity, and carrying its own particular planet
round its own equator, the outermost sphere carrying
the fixed stars. It was necessary to assume that the
axes about which the various spheres revolved should
have circular motions also, and gradually an increased
number of spheres was evolved, the total number re-
quired by Aristotle reaching fifty-five. It may be regarded
as counting in Aristotle's favour that he did consider the
earth to be a sphere and not a flat disc, but he seems to
have thought that the mathematical spheres of Eudoxus
had a real solid existence, and that not only meteors,
shooting stars and aurora, but also comets and the
milky way belong to the atmosphere. His really great
service to science in collating and criticising all that was
known of natural science would have been greater if so

ASTRONOMY BEFORE KEPLER 7

much of the discussion had not been on the exact mean-
ing of words used to describe phenomena, instead of on
the facts and causes of the phenomena themselves.

Aristarchus of Samos seems to have been the first to
suggest that the planets revolved not about the earth but
about the sun, but the idea seemed so improbable that it
was hardly noticed, especially as Aristarchus himself did
not expand it into a treatise.

About this time the necessity for more accurate places
of the sun and moon, and the liberality of the Ptolemys
who ruled Egypt, combined to provide regular observa-
tions at Alexandria, so that, when Hipparchus came upon
the scene, there was a consi'derable amount of material
for him to use. His discoveries marked a great advance
in the science of astronomy. He noted the irregular
motion of the sun, and, to explain it, assumed that it
revolved uniformly not exactly about the earth but about
a point some distance away, called the " excentric "-1
The line joining the centre of the earth to the excentric
passes through the apses of the sun's orbit, where its
distance from the earth is greatest and least. The same
result he could obtain by assuming that the sun moved
round a small circle, whose centre described a larger
circle about the earth ; this larger circle carrying the
other was called the " deferent": so that the actual
motion of the sun was in an epicycle. Of the two
methods of expression Hipparchus ultimately preferred
the second. He applied the same process to the moon
but found that he could depend upon its being right only
at new and full moon. The irregularity at first and third
quarters he left to be investigated by his successors. He
also considered the planetary observations at his disposal
insufficient and so gave up the attempt at a complete
planetary theory. He made improved determinations

1 See Glossary for this and other technical terms.

8 KEPLER

of some of the elements of the motions of the sun and
moon, and discovered the Precession of the Equinoxes,
from the Alexandrian observations which showed that
each year as the sun came to cross the equator at the
vernal equinox it did so at a point about fifty seconds of
arc earlier on the ecliptic, thus producing in 150 years
an unmistakable change of a couple of degrees, or four
times the sun's diameter. He also invented trigonometry.
His star catalogue was due to the appearance of a new
star which caused him to search for possible previous
similar phenomena£ and also to prepare for checking
future ones. No advance was made in theoretical
astronomy for 260 years, the interval between Hip-
parchus and Ptolemy of Alexandria. Ptolemy accepted
the spherical form of the earth but denied its rotation
or any other movement. He made no advance on
Hipparchus in regard to the sun, though the lapse of
time had largely increased the errors of the elements
adopted by the latter. In the case of the moon, how-
ever, Ptolemy traced the variable inequality noticed
sometimes by Hipparchus at first and last quarter, which
vanished when the moon was in apogee or perigee. This
he called the evection, and introduced another epicycle
to represent it. In his planetary theory he found that
the places given by his adopted excentric did not fit,
being one way at apogee and the other at perigee ; so
that the centre of distance must be nearer the earth. He
found it best to assume the centre of distance half-way
between the centre of the earth and the excentric, thus
"bisecting the excentricity ". Even this did not fit in
the case of Mercury, and in general the agreement
between theory and observation was spoilt by the neces-
sity of making all the orbital planes pass through the
centre of the earth, instead of the sun, thus making a
good accordance practically impossible.

After Ptolemy's time very little was heard for many

ASTRONOMY BEFORE KEPLER 9

centuries of any fresh planetary theory, though advances
in some points of detail were made, notably by some of
the Arab philosophers, who obtained improved values
for some of the elements by using better instruments.
From time to time various modifications of Ptolemy's
theory were suggested, but none of any real value. The
Moors in Spain did their share of the work carried on by
their Eastern co-religionists, and the first independent
star catalogue since the time of Hipparchus was made
by another Oriental, Tamerlane's grandson, Ulugh Begh,
who built a fine observatory at Samarcand in the fifteenth
century. In Spain the work was not monopolised by the
Moors, for in the thirteenth century Alphonso of Castile,
with the assistance of Jewish and Christian computers,
compiled the Alphonsine tables, completed in 1252, in
which year he ascended the throne as Alphonso X.
They were long circulated in MS. and were first printed
in 1483, not long before the end of the period of stag-
nation.

Copernicus was born in 1473 at Thorn in Polish
Prussia. In the course of his studies at Cracow and at
several Italian universities, he learnt all that was known
of the Ptolemaic astronomy and determined to reform it.
His maternal uncle, the Bishop of Ermland, having pro-
vided him with a lay canonry in the Cathedral of Frauen-
burg, he had leisure to devote himself to Science. Review-
ing the suggestions of the ancient Greeks, he was struck by
the simplification that would be introduced by reviving
the idea that the annual motion should be attributed to
the earth itself instead of having a separate annual epi-
cycle for each planet and for the sun. Of the seventy
odd circles or epicycles required by the latest form of the
Ptolemaic system, Copernicus succeeded in dispensing
with rather more than half, but he still required thirty-
four, which was the exact number assumed before
the time of Aristotle. His considerations were almost

io KEPLER'

entirely mathematical, his only invasion into physics being
in defence of the " moving earth " against the stock ob-
jection that if the earth moved, loose objects would fly off,
and towers fall. He did not break sufficiently away from
the old tradition of uniform circular motion. Ptolemy's
efforts at exactness were baulked, as we have seen, by the
supposed necessity of all the orbit planes passing through
the earth, and if Copernicus had simply transferred this re-
sponsibility to the sun he would have done better. But he
would not sacrifice the old fetish, and so, the orbit of
the earth being clearly not circular with respect to the
sun, he made all his planetary planes pass through the
centre of the earth's orbit, instead of through the sun,
thus handicapping himself in the same way though not
in the same degree as Ptolemy. His thirty-four circles
or epicycles comprised four for the earth, three for the
moon, seven for Mercury (on account of his highly
eccentric orbit) and five each for the other planets.

It is rather an exaggeration to call the present accepted
system the Copernican system, as it is really due to
Kepler, half a century after the death of Copernicus, but
much credit is due to the latter for his successful attempt
to provide a real alternative for the Ptolemaic system,
instead of tinkering with it. The old geocentric system
once shaken, the way was gradually smoothed for the
heliocentric system, which Copernicus, still hampered by
tradition, did not quite reach. He was hardly a practical
astronomer in the observational sense. His first recorded
observation, of an occultation of Aldebaran, was made in
1497, and he is not known to have made as many as
fifty astronomical observations, while, of the few he did
make and use, at least one was more than half a degree
in error, which would have been intolerable to such an
observer as Hipparchus. Copernicus in fact seems to
have considered accurate observations unattainable with
the instruments at hand. He refused to give any opinion

ASTRONOMY BEFORE KEPLER 11

on the projected reform of the calendar, on the ground
that the motions of the sun and moon were not known
with sufficient accuracy. It is possible that with better
data he might have made much more progress. He was
in no hurry to publish anything, perhaps on account of
possible opposition. Certainly Luther, with his obstinate
conviction of the verbal accuracy of the Scriptures, re-
jected as mere folly the idea of a moving earth, and
Melanchthon thought such; opinions should be prohibited,
but Rheticus, a professor at the Protestant University of
Wittenberg and an enthusiastic pupil of Copernicus,
urged publication, and undertook to see the work through
the press. This, however, he was unable to complete and
another Lutheran, Osiander, to whom he entrusted it,
wrote a preface, with the apparent intention of disarming
opposition, in which he stated that the principles laid down
were only abstract hypotheses convenient for purposes of
calculation. This unauthorised interpolation may have
had its share in postponing the prohibition of the book
by the Church of Rome.

According to Copernicus the earth is only a planet like
the others, and not even the biggest one, while the sun
is the most important body in the system, and the stars
probably too far away for any motion of the earth to
affect their apparent places. The earth in fact is very
small in comparison with the distance of the stars, as
evidenced by the fact that an observer anywhere on the
earth appears to be in the middle of the universe. He
shows that the revolution of the earth will account for
the seasons, and for the stationary points and retrograde
motions of the planets. He corrects definitely the order
of the planets outwards from the sun, a matter which had
been in dispute. A notable defect is due to the idea that
a body can only revolve. about another body or a point,
as if rigidly connected with it, so that, in order to keep
the earth's axis in a constant direction in space, he has

12 KEPLER

to invent a third motion. His discussion of precession,
which he rightly attributes to a slow motion of the earth's
axis, is marred by the idea that the precession is variable.
With all its defects, partly due to reliance on bad ob-
servations, the work showed a great advance in the
interpretation of the motions of the planets ; and his
determinations of the periods both in relation to the earth
and to the stars were adopted by Reinhold, Professor of
Astronomy at Wittenberg, for the new Prutenic or
Prussian Tables, which were to supersede the obsolete
Alphonsine Tables of the thirteenth century.

In comparison with the question of the motion of the
earth, no other astronomical detail of the time seems to
be of much consequence. Comets, such as from time to
time appeared, bright enough for naked eye observation,
were still regarded as atmospheric phenomena, and their
principal interest, as well as that of eclipses and planetary
conjunctions, was in relation to astrology. Reform,
however, was obviously in the air. The doctrine of
Copernicus was destined very soon to divide others besides
the Lutheran leaders. The leaven of inquiry was working,
and not long after the death of Copernicus real advances
were to come, first in the accuracy of observations, and,
as a necessary result of these, in the planetary theory
itself.

CHAPTER II.

EARLY LIFE OF KEPLER.

ON 2 1st December, 1571, at Weil in the Duchy of
Wurtemberg, was born a weak and sickly seven-months'
child, to whom his parents Henry and Catherine Kepler
gave the name of John. Henry Kepler was a petty
officer in the service of the reigning Duke, and in 1 576
joined the army serving in the Netherlands. His wife
followed him, leaving her young son in his grandfather's
care at Leonberg, where he barely recovered from a
severe attack of smallpox. It was from this place that
John derived the Latinised name of Leonmontanus, in
accordance with the common practice of the time, but
he was not known by it to any great extent. He was
sent to school in 1577, but in the following year his
father returned to Germany, almost ruined by the
absconding of an acquaintance for whom he had become
surety. Henry Kepler was obliged to sell his house and
most of his belongings, and to keep a tavern at Elmend-
ingen, withdrawing his son from school to help him with
the rough work. In 1583 young Kepler was sent to the
school at Elmendingen, and in 1584 had another narrow
escape from death by a violent illness. In 1586 he was
sent, at the charges of the Duke, to the monastic school
of Maulbronn ; from whence, in accordance with the
school regulations, he passed at the end of his first year
the examination for the bachelor's degree at Tubingen,
returning for two more years as a " veteran" to Maul-
bronn before being admitted as a resident student at

('3)

14 KEPLER

Tubingen. The three years thus spent at Maulbronn
were marked by recurrences of several of the diseases
from which he had suffered in childhood, and also by
family troubles at his home. His father went away
after a quarrel with his wife Catherine, and died abroad.
Catherine herself, who seems to have been of a very
unamiable disposition, next quarrelled with her own
relatives. It is not surprising therefore that Kepler after
taking his M.A. degree in August, 1591, coming out
second in the examination lists, was ready to accept the
first appointment offered him, even if it should involve
leaving home. This happened to be the lectureship in
astronomy at Gratz, the chief town in Styria. Kepler's
knowledge of astronomy was limited to the compulsory
school course, nor had he as yet any particular leaning
towards the science ; the post, moreover, was a meagre
and unimportant one. On the other hand he had
frequently expressed disgust at the way in which one
after another of his companions had refused " foreign "
appointments which had been arranged for them under
the Duke's scheme of education. His tutors also strongly
urged him to accept the lectureship, and he had not the
usual reluctance to leave home. He therefore proceeded
to Gratz, protesting that he did not thereby forfeit his
claim to a more promising opening, when such should
appear. His astronomical tutor, Maestlin, encouraged
him to devote himself to his newly adopted science, and
the first result of this advice appeared before very long
in Kepler's " Mysterium Cosmographicum ". The bent
of his mind was towards philosophical speculation, to
which he had been attracted in his youthful studies of
Scaliger's "Exoteric Exercises". He says he devoted
much time "to the examination of the nature of heaven,
of souls, of genii, of the elements, of the essence of fire,
of the cause of fountains, the ebb and flow of the tides,
the shape of the continents and inland seas, and things

EARLY LIFE OF KEPLER 15

of this sort ". Following his tutor in his admiration for
the Copernican theory, he wrote an essay on the primary
motion, attributing it to the rotation of the earth, and
this not for the mathematical reasons brought forward
by Copernicus, but, as he himself says, on physical or
metaphysical grounds. In 1595, having more leisure
from lectures, he turned his speculative mind to the
number, size, and motion of the planetary orbits. He
first tried simple numerical relations, but none of them
appeared to be twice, thrice, or four times as great as
another, although he felt convinced that there was some
relation between the motions and the distances, seeing
that when a gap appeared in one series, there was a
corresponding gap in the other. These gaps he attempted
to fill by hypothetical planets between Mars and Jupiter,
and between Mercury and Venus, but this method also
failed to provide the regular proportion which he sought,
besides being open to the objection that on the same
principle there might be many more equally invisible
planets at either end of the series. He was nevertheless
unwilling to adopt the opinion of Rheticus that the
number six was sacred, maintaining that the "sacred-
ness " of the number was of much more recent date than
the creation of the worlds, and could not therefore account
for it. He next tried an ingenious idea, comparing the
perpendiculars from different points of a quadrant of a
circle on a tangent at its extremity. The greatest of
these, the tangent, not being cut by the quadrant, he
called the line of the sun, and associated with infinite
force. The shortest, being the point at the other end of
the quadrant, thus corresponded to the fixed stars or zero
force ; intermediate ones were to be found proportional
to the " forces " of the six planets. After a great amount
of unfinished trial calculations, which took nearly a
whole summer, he convinced himself that success did not
lie that way. In July, 1595, while lecturing on the

16 KEPLER

great planetary conjunctions, he drew quasi-triangles in
a circular zodiac showing the slow progression of these
points of conjunction at intervals of just over 240° or
eight signs. The successive chords marked out a smaller
circle to which they were tangents, about half the diameter
of the zodiacal circle as drawn, and Kepler at once saw
a similarity to the orbits of Saturn and Jupiter, the
radius of the inscribed circle of an equilateral triangle
being half that of the circumscribed circle. His natural
sequence of ideas impelled him to try a square, in the
hope that the circumscribed and inscribed circles might
give him a similar "analogy" for the orbits of Jupiter
and Mars. He next tried a pentagon and so on, but he
soon noted that he would never reach the sun that way,
nor would he find any such limitation as six, the number
of "possibles" being obviously infinite. The actual
planets morever were not even six but only five, so far
as he knew, so he next pondered the question of what
sort of things these could be of which only five different
figures were possible and suddenly thought of the five
regular solids.1 * He immediately pounced upon this idea
and ultimately evolved the following scheme. " The
earth is the sphere, the measure of all ; round it describe
a dodecahedron ; the sphere including this will be Mars.
Round Mars describe a tetrahedron ; the sphere including
this will be Jupiter. Describe a cube round Jupiter ;
the sphere including this will be Saturn. Now, inscribe
in the earth an icosahedron, the sphere inscribed in it
will be Venus : inscribe an octahedron in Venus : the

1 Since the sum of the plane angles at a corner of a regular solid must
be less than four right angles, it is easily seen that few regular solids are
possible. Hexagonal faces are clearly impossible, or any polygonal faces
with more than five sides. The possible forms are the dodecahedron with
twelve pentagonal faces, three meeting at each corner ; the cube, six square
faces, three meeting at each corner; and three figures with triangular
faces, the tetrahedron of four faces, three meeting at each corner ; the
octahedron of eight faces, four meeting at each corner ; and the icosahedron
of twenty faces, five meeting at each corner.

EARLY LIFE OF KEPLER 17

circle inscribed in it will be Mercury." With this result
Kepler was inordinately pleased, and regretted not a
moment of the time spent in obtaining it, though to us
this "Mysterium Cosmographicum " can only appear,
useless, even without the more recent additions to the
known planets. He admitted that a certain thickness
must be assigned to the intervening spheres to cover
the greatest and least distances of the several planets
from the sun, but even then some of the numbers obtained
are not a very close fit for the corresponding planetary
orbits. Kepler's own suggested explanation of the
discordances was that they must be due to erroneous
measures of the planetary distances, and this, in those
days of crude and infrequent observations, could not
easily be disproved. He next thought of a variety of
reasons why the five regular solids should occur in pre-
cisely the order given and in no other, diverging from
this into a subtle and not very intelligible process of
reasoning to account for the division of the zodiac into
360°. The next subject was more important, and dealt
with the relation between the distances of the planets
and their times of revolution round the sun. It was
obvious that the period was not simply proportional to
the distance, as the outer planets were all too slow for
this, and he concluded "either that the moving intelli-
gences of the planets are weakest in those that are
farthest from the sun, or that there is one moving
intelligence in the sun, the common centre, forcing them
all round, but those most violently which are nearest,
and that it languishes in some sort and grows weaker
at the most distant, because of the remoteness and the
attenuation of the virtue ". This is not so near a guess
at the theory of gravitation as might be supposed, for
Kepler imagined that a repulsive force was necessary to
account for the planets being sometimes further from
the sun, and so laid aside the idea of a constant attractive

1 8 KEPLER

force. He made several other attempts to find a law
connecting the distances and periods of the planets, but
without success at that time, and only desisted when by
unconsciously arguing in a circle he appeared to get the
same result from two totally different hypotheses. He
sent copies of his book to several leading astronomers, of
whom Galileo praised his ingenuity and good faith, while
Tycho Brahe was evidently much struck with the work
and advised him to adapt something similar to the
Tychonic system instead of the Copernican. He also
intimated that his Uraniborg observations would provide
more accurate determinations of the planetary orbits,
and thus made Kepler eager to visit him, a project which
as we shall see was more than fulfilled. Another copy of
the book Kepler sent to Reymers the Imperial astronomer
with a most fulsome letter, which Tycho, who asserted
that Reymers had simply plagiarised his work, very
strongly resented, thus drawing from Kepler a long letter
of apology. About the same time Kepler had married
a lady already twice widowed, and become involved in
difficulties with her relatives on financial grounds, and
with the Styrian authorities in connection with the
religious disputes then coming to a head. On account
of these latter he thought it expedient, the year after his
marriage, to withdraw to Hungary, from whence he sent
short treatises to Tubingen, " On the magnet " (following
the ideas of Gilbert of Colchester), " On the cause of the
obliquity of the ecliptic " and " On the Divine wisdom as
shown in the Creation ". His next important step makes
it desirable to devote a chapter to a short notice of Tycho
Brahe.

CHAPTER III.

TYCHO BRAKE.

THE age following that of Copernicus produced three
outstanding figures associated with the science of astro-
nomy, then reaching the close of what Professor Forbes
so aptly styles the geometrical period. These three
Sir David Brewster has termed "Martyrs of Science" ;
Galileo, the great Italian philosopher, has his own place
among the "Pioneers of Science" ; and invaluable though
Tycho Brahe's work was, the latter can hardly be claimed
as a pioneer in the same sense as the other two. Never-
theless, Kepler, the third member of the trio, could not
have made his most valuable discoveries without Tycho's
observations.

Of noble family, born a twin on I4th December, 1546,
at Knudstrup in Scania (the southernmost part of Sweden,
then forming part of the kingdom of Denmark), Tycho
was kidnapped a year later by a childless uncle. This
uncle brought him up as his own son, provided him at
the age of seven with a tutor, and sent him in 1559 to
the University of Copenhagen, to study for a political
career by taking courses in rhetoric and philosophy. On
2 1st August, 1560, however, a solar eclipse took place,
total in Portugal, and therefore of small proportions in
Denmark, and Tycho's keen interest was awakened, not
so much by the phenomenon, as by the fact that it had
occurred according to prediction. Soon afterwards he
purchased an edition of Ptolemy in order to read up the

20 KEPLER

subject of astronomy, to which, and to mathematics, he
devoted most of the remainder of his three years' course
at Copenhagen. His uncle next sent him to Leipzig to
study law, but he managed to continue his astronomical
researches. He obtained the Alphonsine and the new
Prutenic Tables, but soon found that the latter, though
more accurate than the former, failed to represent the
true positions of the planets, and grasped the fact that
continuous observation was essential in order to determine
the true motions. He began by observing a conjunction
of Jupiter and Saturn in August, 1563, and found the
Prutenic Tables several days in error, and the Alphonsine
a whole month. He provided himself with a cross-staff
for determining the angular distance between stars or
other objects, and, finding the divisions of the scale in-
accurate, constructed a table of corrections, an improve-
ment that seems to have been a decided innovation, the
previous practice having been to use the best available
instrument and ignore its errors. About this time war
broke out between Denmark and Sweden, and Tycho
returned to his uncle, who was vice-admiral and attached
to the king's suite. The uncle died in the following
month, and early in the next year Tycho went abroad
again, this time to Wittenberg. After five months, how-
ever, an outbreak of plague drove him away, and he
matriculated at Rostock, where he found little astronomy
but a good deal of astrology. While there he fought a
duel in the dark and lost part of his nose, which he re-
placed by a composition of gold and silver. He carried
on regular observations with his cross-staff and persevered
with his astronomical studies in spite of the objections
and want of sympathy of his fellow-countrymen. The
King of Denmark, however, having a higher opinion of
the value of science, promised Tycho the first canonry
that should fall vacant in the cathedral chapter of Ros-
kilde, so that he might be assured of an income while

TYCHO BRAHE 21

devoting himself to financially unproductive work. In
1568 Tycho left Rostock, and matriculated at Basle, but
soon moved on to Augsburg, where he found more
enthusiasm for astronomy, and induced one of his new
friends to order the construction of a large I Q-foot quad-
rant of heavy oak beams. This was the first of the series
of great instruments associated with Tycho's name, and
it remained in use for five years, being destroyed by a
great storm in 1574. Tycho meanwhile had left Augs-
burg in 1570 and returned to live with his father, now
governor of Helsingborg Castle, until the latter's death
in the following year. Tycho then joined his mother's
brother, Steen Bille, the only one of his relatives who
showed any sympathy with his desire for a scientific
career.

On nth November, 1 572, Tycho noticed an unfamiliar
bright star in the constellation of Cassiopeia, and con-
tinued to observe it with a sextant. It was a very
brilliant object, equal to Venus at its brightest for the
rest of November, not falling below the first magnitude
for another four months, and remaining visible for more
than a year afterwards. Tycho wrote a little book on
the new star, maintaining that it had practically no
parallax, and therefore could not be, as some supposed,
a comet. Deeming authorship beneath the dignity of a
noble he was very reluctant to publish, but he was con-
vinced of the importance of increasing the number and
accuracy of observations, though he was by no means free
from all the erroneous ideas of his time. The little book
contained a certain amount of astrology, but Tycho evi-
dently did not regard this as of very great importance. He
adopted the view that the very rarity of the phenomenon
of a new star must prevent the formulation and adoption
of definite rules for determining its significance. We
gather from lectures which he was persuaded to deliver at
Ihe University of Copenhagen that, though in agreement

22 KEPLER

with the accepted canons of astrology as to the influ-
ence of planetary conjunctions and such phenomena on
the course of human events, he did not consider the fate
predicted by any one's horoscope to be unavoidable, but
thought the great value of astrology lay in the warnings
derived from such computations, which should enable
the believer to avoid threatened calamities. In 1575 he
left Denmark once more and made his way to Cassel,
where he found a kindred spirit in the studious Landgrave,
William IV. of Hesse, whose astronomical pursuits had
been interrupted by his accession to the government of
Hesse, in 1 567. Tycho observed with him for some time,
the two forming a firm friendship, and then visited
successively Frankfort, Basle, and Venice, returning by
way of Augsburg, Ratisbon, and Saalfeld to Wittenberg ;
on the way he acquired various astronomical manuscripts,
made friends among practical astronomers, and examined
new instruments. He seemed to have considered the
advantages of the several places thus visited and decided
on Basle, but on his return to Denmark to fetch his
family with the object of transferring them to Basle, he
found that his friend the Landgrave had written to King
Frederick on his behalf, urging him to provide the means
to enable Tycho to pursue his astronomical work, pro-
mising that not only should credit result for the king and
for Denmark but that science itself would be greatly ad-
vanced. The ultimate result of this letter was that after
refusing various offers, Tycho accepted from the king a
grant of the small island of Hveen, in the Sound, with a
guaranteed income, in addition to a large sum from the
treasury for building an observatory on the island, far
removed from the distractions of court life. Here Tycho
built his celebrated observatory of Uraniborg and began
observations in December, 1576, using the large instru-
ments then found necessary in order to attain the accuracy
of observation which within the next half-century was to

TYCHO BRAKE 23

be so greatly facilitated by the invention of the telescope.
Here also he built several smaller observing rooms, so
that his pupils should be able to observe independently.
For more than twenty years he continued his observations
at Uraniborg, surrounded by his family, and attracting
numerous pupils. His constant aim was to accumulate
a large store of observations of a high order of accuracy,
and thus to provide data for the complete reform of
astronomy. As we have seen, few of the Danish nobles
had any sympathy with Tycho's pursuits, and most of
them strongly resented the continual expense borne by
the King's treasury. Tycho moreover was so absorbed
in his scientific pursuits that he would not take the trouble
to be a good landlord, nor to carry out all the duties laid
upon him in return for certain of his grants of income.
His buildings included a chemical laboratory, and he was
in the habit of making up elixirs for various medical
purposes ; these were quite popular, particularly as he
made no charge for them. He seems to have been some-
thing of a homceopathist, for he recommends sulphur
to cure infectious diseases " brought on by the sulphurous
vapours of the Aurora Borealis " !

King Frederick, in consideration of various grants to
Tycho, relied upon his assistance in scientific matters, and
especially in astrological calculations ; such as the horo-
scope of the heir apparent, Prince Christian, born in 1 577,
which has been preserved among Tycho's writings. There
is, however, no known copy in existence of any of the
series of annual almanacs with predictions which he pre-
pared for the King. In November, 1577, appeared a
bright comet, which Tycho carefully observed with his
sextant, proving that it had no perceptible parallax, and
must therefore be further off than the moon. He thus
definitely overthrew the common belief in the atmos-
pheric origin of comets, which he had himself hitherto
shared With increasing accuracy he observed several

24 KEPLER

other comets, notably one in 1585, when he had a full
equipment of instruments and a large staff of assistants.
The year 1588, which saw the death of his royal bene-
factor, saw also the publication of a volume of Tycho's
great work " Introduction to the New Astronomy ". The
first volume, devoted to the new star of 1572, was not
ready, because the reduction of the observations involved
so much research to correct the star places for refraction,
precession, etc. ; it was not completed in fact until Tycho's
death, but the second volume, dealing with the comet of
1577, was printed at Uraniborg and some copies were
issued in 1588. Besides the comet observations it in-
cluded an account of Tycho's system of the world. He
would not accept the Copernican system, as he considered
the earth too heavy and sluggish to move, and also that
the authority of Scripture was against such an hypothesis.
He therefore assumed that the other planets revolved
about the sun, while the sun, moon, and stars revolved
about the earth as a centre. Geometrically this is much
the same as the Copernican system, but physically
it involves the grotesque demand that the whole system
of stars revolves round our insignificant little earth every
twenty-four hours. Since his previous small book on the
comet, Tycho had evidently considered more fully its
possible astrological significance, for he foretold a religious
war, giving the date of its commencement, and also the
rising of a great Protestant champion. These predictions
were apparently fulfilled almost to the letter by the
great religious wars that broke out towards the end of
the sixteenth century, and in the person of Gustavus
Adolphus.

King Frederick's death did not at first affect Tycho's
position, for the new king, Christian, was only eleven
years old, and for some years the council of regents in-
cluded two of his supporters. After their deaths, however,
his emoluments began to be cut down on the plea of

TYCHO BRAKE 25

economy, and as he took very little trouble to carry out
any other than scientific duties it was easy enough for
his enemies to find fault. One after another source of
income was cut off, but he persevered with his scientific
work, including a catalogue of stars. He had obtained
plenty of good observations of 777 stars, but thought his
catalogue should contain 1000 stars, so he hastily ob-
served as many more as he could up to the time of his
leaving Hveen, though even then he had not completed
his programme. About the time that King Christian
reached the age of eighteen, Tycho began to look about
for a new patron, and to consider the prospects offered
by transferring himself with his instruments and activities
to the patronage of the Emperor Rudolph II. In 1597,
when even his pension from the Royal treasury was cut
off, he hurriedly packed up his instruments and library,
and after a few weeks' sojourn at Copenhagen, proceeded
to Rostock, in Mecklenburg, whence he sent an appeal
to King Christian. It is possible that had he done this
before leaving Hveen it might have had more effect, but
it can be readily seen from the tone of the king's un-
favourable reply that his departure was regarded as an
aggravation of previous shortcomings. Driven from
Rostock by the plague, Tycho settled temporarily at
Wandsbeck, in Holstein, but towards the end of 1598 set
out to meet the Emperor at Prague. Once more plague
intervened and he spent some time at Dresden, afterwards
going to Wittenberg for the winter. He ultimately
reached Prague in June, 1 599. Rudolph granted him a
salary of at least 3000 florins, promising also to settle on
him the first hereditary estate that should lapse to the
Crown. He offered, moreover, the choice between three
castles outside Prague, of which Tycho chose Benatek.
There he set about altering the buildings in readiness for
his instruments, for which he sent to Uraniborg. Before
they reached him, after many vexatious delays, he had

26 KEPLER

given up waiting for the funds promised for his building
expenses, and removed from Benatek to Prague, It was
during this interval that after considerable negotiation,
Kepler, who had been in correspondence with Tycho,
consented to join him as an assistant. Another assistant,
Longomontanus, who had been with Tycho at Uraniborg,
was finding difficulty with the long series of Mars obser-
vations, and it was arranged that he should transfer his
energies to the lunar observations, leaving those of Mars
for Kepler. Before very much could be done with them,
however, Tycho died at the end of October, 1601. He
may have regretted the peaceful island of Hveen, consider-
ing the troubles in which Bohemia was rapidly becoming
involved, but there is little doubt that had it not been for
his self-imposed exile, his observations would not have
come into Kepler's hands, and their great value might
have been lost. In any case it was at Uraniborg that
the mass of observations was produced upon which the
fame of Tycho Brahe rests. His own discoveries, though
in themselves the most important made in astronomy for
many centuries, are far less valuable than those for which
his observations furnished the material. He discovered
the third and fourth inequalities of the moon in longitude,
called respectively the variation and the annual equation,
also the variability of the motion of the moon's nodes
and the inclination of its orbit to the ecliptic. He ob-
tained an improved value of the constant of precession,
and did good service by rejecting the idea that it was
variable, an idea which, under the name of trepidation,
had for many centuries been accepted. He discovered
the effect of refraction, though only approximately its
amount, and determined improved values of many
other astronomical constants, but singularly enough
made no determination of the distance of the sun, adopt-
ing instead the ancient and erroneous value given by
Hipparchus.

TYCHO BRAHE 27

His magnificent Observatory of Uraniborg, the finest
building for astronomical purposes that the world had
hitherto seen, was allowed to fall into decay, and scarcely
more than mere indications of the site may now be
seen.

CHAPTER IV.

KEPLER JOINS TYCHO.

THE association of Kepler with Tycho was one of the
most important landmarks in the history of astronomy.
The younger man hoped, by the aid of Tycho' s planetary
observations, to obtain better support for some of his
fanciful speculative theories, while the latter, who had
certainly not gained in prestige by leaving Denmark,
was in great need of a competent staff of assistants. Of
the two it would almost seem that Tycho thought
himself the greater gainer, for in spite of his reputation
for brusqueness and want of consideration, he not only
made light of Kepler's apology in the matter of Reymers,
but treated him with uniform kindness in the face of
great rudeness and ingratitude. He begged him to come
" as a welcome friend," though Kepler, very touchy on
the subject of his own astronomical powers, was afraid
he might be regarded as simply a subordinate assistant.
An arrangement had been suggested by which Kepler
should obtain two years' leave of absence from Gratz on
full pay, which, because of the higher cost of living in
Prague, should be supplemented by the Emperor ; but
before this could be concluded, Kepler threw up his
professorship, and thinking he had thereby also lost the
chance of going to Prague, applied to Maestlin and
others of his Tubingen friends to make interest for him
with the Duke of Wurtemberg and secure the professor-
ship of medicine. Tycho, however, still urged him to
come to Prague, promising to do his utmost to secure

(28)

KEPLER JOINS TYCHO 29

for him a permanent appointment, or in any event to
see that he was not the loser by coming. Kepler was
delayed by illness on the way, but ultimately reached
Prague, accompanied by his wife, and for some time
lived entirely at Tycho's expense, writing by way of
return essays against Reymers and another man, who
had claimed the credit of the Tychonic system. This
Kepler could do with a clear conscience, as it was only
a question of priority and did not involve any support of
the system, which he deemed far inferior to that of
Copernicus. The following year saw friction between
the two astronomers, and we learn from Kepler's abject
letter of apology that he was entirely in the wrong. It
was about money matters, which in one way or another
embittered the rest of Kepler's life, and it arose during
his absence from Prague. On his return in September,
1 60 1, Tycho presented him to the Emperor, who gave
him the title of Imperial Mathematician, on condition of
assisting Tycho in his calculations, the very thing Kepler
was most anxious to be allowed to do : for nowhere
else in the world was there such a collection of good
observations sufficient for his purpose of reforming the
whole theory of astronomy. The Emperor's interest was
still mainly with astrology, but he liked to think that his
name would be handed down to posterity in connection
with the new Planetary Tables in the same way as that
of Alphonso of Castile, and he made liberal promises to
pay the expenses. Tycho's other principal assistant,
Longomontanus, did not stay long after giving up the
Mars observations to Kepler, but instead of working at
the new lunar theory, suddenly left to take up a professor- -
ship of astronomy in his native Denmark. Very shortly
afterwards Tycho himself died of acute distemper ; Kepler
began to prepare the mass of manuscripts for publication,
but, as everything was claimed by the Brahe family, he
was not allowed to finish the work. He succeeded to

30 KEPLER

Tycho's post of principal mathematician to the Emperor,
at a reduced official salary, which owing to the emptiness
of the Imperial treasury was almost always in arrear. In
order to meet his expenses he had recourse to the casting
of nativities, for which he gained considerable reputation
and received very good pay. He worked by the con-
ventional rules of astrology, and was quite prepared to
take fees for so doing, although he had very little faith
in them, preferring his own fanciful ideas.

In 1604 the constellation of Cassiopeia was once more
temporarily enriched by the appearance of a new star,
said by some to be brighter than Tycho's nova, and by
others to be twice as bright as Jupiter. Kepler at once
wrote a short account of it, from which may be gathered
some idea of his attitude towards astrology. Contrasting
the two novae, he says : " Yonder one chose for its ap-
pearance a time no way remarkable, and came into the
world quite unexpectedly, like an enemy storming a town
and breaking into the market-place before the citizens are
aware of his approach ; but ours has come exactly in the
year of which astrologers have written so much about
the fiery trigon that happens in it ; just in the month in
which (according to Cyprian), Mars comes up to a very
perfect conjunction with the other two superior planets ;
just in the day when Mars has joined Jupiter, and just in
the region where this conjunction has taken place. There-
fore the apparition of this star is not like a secret hostile
irruption, as was that one of 1572, but the spectacle of a
public triumph, or the entry of a mighty potentate ;
when the couriers ride in some time before to prepare his
lodgings, and the crowd of young urchins begin to think
the time over long to wait, then roll in, one after another,
the ammunition and money, and baggage waggons, and
presently the trampling of horse and the rush of people
from every side to the streets and windows ; and when
the crowd have gazed with their jaws all agape at the

KEPLER JOINS TYCHO 31

troops of knights ; then at last the trumpeters and archers
and lackeys so distinguish the person of the monarch,
that there is no occasion to point him out, but every one
cries of his own accord — ' Here we have him '. What
it may portend is hard to determine, and this much only
is certain, that it comes to tell mankind either nothing at
all or high and mighty news, quite beyond human sense
and understanding. It will have an important influence
on political and social relations ; not indeed by its own
nature, but as it were accidentally through the disposition
of mankind. First, it portends to the booksellers great
disturbances and tolerable gains ; for almost every
Theologus, Philosophicus, Medicus, and Mathematicus, or
whoever else, having no laborious occupation entrusted
to him, seeks his pleasure in studiis, will make particular
remarks upon it, and will wish to bring these remarks to
the light. Just so will others, learned and unlearned,
wish to know its meaning, and they will buy the authors
who profess to tell them. I mention these things merely
by way of example, because although thus much can be
easily predicted without great skill, yet may it happen
just as easily, and in the same manner, that the vulgar,
or whoever else is of easy faith, or, it may be, crazy, may
wish to exalt himself into a great prophet; or it may
even happen that some powerful lord, who has good
foundation and beginning of great dignities, will be
cheered on by this phenomenon to venture on some new
scheme, just as if God had set up this star in the dark-
ness merely to enlighten them." He made no secret of
his views on conventional astrology, as to which he
claimed to speak with the authority of one fully con-
versant with its principles, but he nevertheless expressed
his sincere conviction that the conjunctions and aspects
of the planets certainly did affect things on the earth,
maintaining that he was driven to this belief against his
will by "most unfailing experiences".

32 KEPLER

Meanwhile the projected Rudolphine Tables were con-
tinually delayed by the want of money. Kepler's nominal
salary should have been ample for his expenses, increased
though they were by his growing family, but in the
depleted state of the treasury there were many who ob-
jected to any payment for such " unpractical " purposes.
This particular attitude has not been confined to any
special epoch or country, but the obvious result in Kepler's
case was to compel him to apply himself to less expensive
matters than the Planetary Tables, and among these must
be included not only the horoscopes or nativities, which
owing to his reputation were always in demand, but also
other writings which probably did not pay so well. In
1604 he published "A Supplement to Vitellion," contain-
ing the earliest known reasonable theory of optics, and
especially of dioptrics or vision through lenses. He
compared the mechanism of the eye with that of Porta's
" Camera Obscura," but made no attempt to explain how
the image formed on the retina is understood by the
brain. He went carefully into the question of refraction,
the importance of which Tycho had been the first astro-
nomer to recognise, though he only applied it at low
altitudes, and had not arrived at a true theory or accurate
values. Kepler wasted a good deal of time and ingenuity
on trial theories. He would invariably start with some
hypothesis, and work out the effect. He would then test
it by experiment, and when it failed would at once re-
cognise that his hypothesis was a priori bound to fail.
He rarely seems to have noticed the fatal objections in
time to save himself trouble. He would then at once
start again on a new hypothesis, equally gratuitous and
equally unfounded. It never seems to have occurred to
him that there might be a better way of approaching a
problem. Among the lines he followed in this particular
investigation were, first, that refraction depends only on
the angle of incidence, which, he says, cannot be correct

KEPLER JOINS TYCHO 33

as it would thus be the same for all refracting substances ;
next, that it depended also on the density of the medium.
This was a good shot, but he unfortunately assumed that
all rays passing into a denser medium would apparently
penetrate it to a depth depending only on the medium,
which means that there is a constant ratio between the
tangents, instead of the sines, of the inclination of the
incident and refracted rays to the normal. Experiment
proved that this gave too high values for refraction near
the vertical compared with those near the horizon, so
Kepler " went off at a tangent " and tried a totally new
set of ideas, which all reduced to the absurdity of a re-
fraction which vanished at the horizon. These were
followed by another set, involving either a constant
amount of refraction or one becoming infinite. He then
came to the conclusion that these geometrical methods
must fail because the refracted image is not real, and
determined to try by analogy only, comparing the equally
unreal image formed by a mirror with that formed by re-
fraction in water. He noticed how the bottom of a
vessel containing water appears to rise more and more
away from the vertical, and at once jumped to the ana-
logy of a concave mirror, which magnifies the image,
while a convex mirror was likened to a rarer medium.
This line of attack also failed him, as did various
attempts to find relations between his measurements of
refraction and conic sections, and he broke off suddenly
with a diatribe against Tycho's critics, whom he likened
to blind men disputing about colours. Not many years
later Snell discovered the true law of refraction, but
Kepler's contribution to the subject, though he failed to
discover the actual law, includes several of the adopted
" by-laws ". He noted that atmospheric refraction would
alter with the height of the atmosphere and with tempera-
ture, and also recognised the fact that rainbow colours
depend on the angle of refraction, whether seen in the

3

34 KEPLER

rainbow itself, or in dew, glass, water, or any similar
medium. He thus came near to anticipating Newton.
Before leaving the subject of Kepler's optics it will be
well to recall that a few years later after hearing of
Galileo's telescope, Kepler suggested that for astronomical
purposes two convex lenses should be used, so that there
should be a real image where measuring wires could be
placed for reference. He did not carry out the idea him-
self, and it was left to the Englishman Gascoigne to
produce the first instrument on this " Keplerian " principle,
universally known as the Astronomical Telescope.

In 1606 came a second treatise on the new star, dis-
cussing various theories to account for its appearance,
and refusing to accept the notion that it was a " fortuitous
concourse of atoms". This was followed in 1607 by a
treatise on comets, suggested by the comet appearing
that year, known as Halley's comet after its next return.
He regarded comets as "planets" moving in straight
lines, never having examined sufficient observations of
any comet to convince himself that their paths are curved.
If he had not assumed that they were external to the
system and so could not be expected to return, he might
have anticipated Halley's discovery. Another suggestive
remark of his was to the effect that the planets must be
self-luminous, as otherwise Mercury and Venus, at any
rate, ought to show phases. This was put to the test
not long afterwards by means of Galileo's telescope.

In 1607 Kepler rushed into print with an alleged
observation of Mercury crossing the sun, but after
Galileo's discovery of sun-spots, Kepler at once cheer-
fully retracted his observation of " Mercury," and so far
was he from being annoyed or bigoted in his views,
that he warmly adopted Galileo's side, in contrast to
most of those whose opinions were liable to be over-
thrown by the new discoveries. Maestlin and others of
Kepler's friends took the opposite view.

CHAPTER V.

KEPLER'S LAWS.

WHEN Gilbert of Colchester, in his " New Philosophy,"
founded on his researches in magnetism, was dealing
with tides, he did not suggest that the moon attracted
the water, but that " subterranean spirits and humours,
rising in sympathy with the moon, cause the sea also to
rise and flow to the shores and up rivers ". It appears
that an idea, presented in some such way as this, was
more readily received than a plain statement. This so-
called philosophical method was, in fact, very generally
applied, and Kepler, who shared Galileo's admiration for
Gilbert's work, adopted it in his own attempt to extend
the idea of magnetic attraction to the planets. The
general idea of " gravity" opposed the hypothesis of the
rotation of the earth on the ground that loose objects
would fly off : moreover, the latest refinements of the old
system of planetary motions necessitated their orbits
being described about a mere empty point. Kepler
very strongly combated these notions, pointing out the
absurdity of the conclusions to which they tended, and
proceeded in set terms to describe his own theory.

"Every corporeal substance, so far forth as it is
corporeal, has a natural fitness for resting in every
place where it may be situated by itself beyond the
sphere of influence of a body cognate with it. Gravity
is a mutual affection between cognate bodies towards
union or conjunction (similar in kind to the magnetic
virtue), so that the earth attracts a stone much rather

(35)

36 KEPLER

than the stone seeks the earth. Heavy bodies (if we
begin by assuming the earth to be in the centre of the
world) are not carried to the centre of the world in its
quality of centre of the world, but as to the centre of a
cognate round body, namely, the earth ; so that where-
soever the earth may be placed, or whithersoever it may
be carried by its animal faculty, heavy bodies will always
be carried towards it. If the earth were not round, heavy
bodies would not tend from every side in a straight
line towards the centre of the earth, but to different
points from different sides. If two stones were placed
in any part of the world near each other, and beyond the
sphere of influence of a third cognate body, these stones,
like two magnetic needles, would come together in the
intermediate point, each approaching the other by a space
proportional to the comparative mass of the other. If
the moon and earth were not retained in their orbits by
their animal force or some other equivalent, the earth
would mount to the moon by a fifty-fourth part of their
distance, and the moon fall towards the earth through the
other fifty-three parts, and they would there meet, assum-
ing, however, that the substance of both is of the same
density. If the earth should cease to attract its waters
to itself all the waters of the sea would he raised and
would flow to the body of the moon. The sphere of the
attractive virtue which is in the moon extends as far as
the earth, and entices up the waters ; but as the moon
flies rapidly across the zenith, and the waters cannot
follow so quickly, a flow of the ocean is occasioned in
the torrid zone towards the westward. If the attractive
virtue of the moon extends as far as the earth, it follows
with greater reason that the attractive virtue of the earth
extends as far as the moon and much farther; and, in
short, nothing which consists of earthly substance any-
how constituted although thrown up to any height, can
ever escape the powerful operation of this attractive

KEPLER'S LAWS 37

virtue. Nothing which consists of corporeal matter is
absolutely light, but that is comparatively lighter which
is rarer, either by its own nature, or by accidental heat.
And it is not to be thought that light bodies are escaping
to the surface of the universe while they are carried up-
wards, or that they are not attracted by the earth. They
are attracted, but in a less degree, and so are driven out-
.wards by the heavy bodies ; which being done, they stop,
and are kept by the earth in their own place. But
although the attractive virtue of the earth extends up-
wards, as has been said, so very far, yet if any stone
should be at a distance great enough to become sensible
compared with the earth's diameter, it is true that on the
motion of the earth such a stone would not follow alto-
gether ; its own force of resistance would be combined with
the attractive force of the earth, and thus it would ex-
tricate itself in some degree from the motion of the earth."
""The above passage from the Introduction to Kepler's
" Commentaries on the Motion of Mars," always regarded
as his most valuable work, must have been known to
Newton, so that no such incident as the fall of an apple
was required to provide a necessary and sufficient ex-
planation of the genesis of his Theory of Universal Gravi-
tation. Kepler's glimpse at such a theory could have
been no more than a glimpse, for he went no further with
it. This seems a pity, as it is far less fanciful than many
of his ideas, though not free from the " virtues" and
t( animal faculties," that correspond to Gilbert's "spirits
and humours". We must, however, proceed to the sub-
ject of Mars, which was, as before noted, the first im-
portant investigation entrusted to Kepler on his arrival
at Prague.

The time taken from one opposition of Mars to the
next is decidedly unequal at different parts of his orbit,
so that many oppositions must be used to determine
the mean motion. The ancients had noticed that what

38 KEPLER

was called the " second inequality," due as we now know
to the orbital motion of the earth, only vanished when
earth, sun, and planet were in line, i.e. at the planet's
opposition ; therefore they used oppositions to determine
the mean motion, but deemed it necessary to apply a
correction to the true opposition to reduce to mean op-
position, thus sacrificing part of the advantage of using
oppositions. Tycho and Longomontanus had followed
this method in their calculations from Tycho's twenty
years' observations. Their aim was to find a position of
the " equant," such that these observations would show
a constant angular motion about it ; and that the com-
puted positions would agree in latitude and longitude
with the actual observed positions. When Kepler arrived
he was told that their longitudes agreed within a couple
of minutes of arc, but that something was wrong with
the latitudes. He found, however, that even in longitude
their positions showed discordances ten times as great
as they admitted, and so, to clear the ground of assump-
tions as far as possible, he determined to use true op-
positions. To this Tycho objected, and Kepler had great
difficulty in convincing him that the new move would be
any improvement, but undertook to prove to him by
actual examples that a false position of the orbit could
by adjusting the equant be made to fit the longitudes
within five minutes of arc, while giving quite erroneous
values of the latitudes and second inequalities. To avoid
the possibility of further objection he carried out this
demonstration separately for each of the systems of
Ptolemy, Copernicus, and Tycho. For the new method
he noticed that great accuracy was required in the reduc-
tion of the observed places of Mars to the ecliptic, and
for this purpose the value obtained for the parallax by
Tycho's assistants fell far short of the requisite accuracy.
Kepler therefore was obliged to recompute the parallax
from the original observations, as also the position of the

KEPLER'S LAWS 39

line of nodes and the inclination of the orbit. The last
he found to be constant, thus corroborating his theory
that the plane of the orbit passed through the sun. He
repeated his calculations no fewer than seventy times
(and that before the invention of logarithms), and at
length adopted values for the mean longitude and longi-
tude of aphelion. He found no discordance greater than
two minutes of arc in Tycho's observed longitudes in
opposition, but the latitudes, and also longitudes in other
parts of the orbit were much more discordant, and he
found to his chagrin that four years' work was practically
wasted. Before making a fresh start he looked for some
simplification of the labour ; and determined to adopt
Ptolemy's assumption known as the principle of the
bisection of the excentricity. Hitherto, since Ptolemy
had given no reason for this assumption, Kepler had
preferred not to make it, only taking for granted that
the centre was at some point on the line called the
excentricity (see Figs, i, 2).

A marked improvement in residuals was the result of
this step, proving, so far, the correctness of Ptolemy's
principle, but there still remained discordances amounting
to eight minutes of arc. Copernicus, who had no idea
of the accuracy obtainable in observations, would prob-
ably have regarded such an agreement as remarkably
good ; but Kepler refused to admit the possibility of an
error of eight minutes in any of Tycho's observations.
He thereupon vowed to construct from these eight
minutes a new planetary theory that should account for
them all. His repeated failures had by this time con-
vinced him that no uniformly described circle could pos-
sibly represent the motion of Mars. Either the orbit
could not be circular, or else the angular velocity could
not be constant about any point whatever. He deter-
mined to attack the " second inequality," i.e. the optical
illusion caused by the earth's annual motion, but first

40 KEPLER

revived an old idea of his own that for the sake of uni-
formity the sun, or as he preferred to regard it, the earth,
should have an equant as well as the planets. From the
irregularities of the solar motion he soon found that this
was the case, and that the motion was uniform about a
point on the line from the sun to the centre of the earth's
orbit, such that the centre bisected the distance from
the sun to the " Equant " ; this fully supported Ptolemy's
principle. Clearly then the earth's linear velocity could
not be constant, and Kepler was encouraged to revive
another of his speculations as to a force which was weaker
at greater distances. He found the velocity greater at
the nearer apse, so that the time over an equal arc at
either apse was proportional to the distance. He con-
jectured that this might prove to be true for arcs at all
parts of the orbit, and to test this he divided the orbit
into 360 equal parts, and calculated the distances to the
points of division. Archimedes had obtained an ap-
proximation to the area of a circle by dividing it radially
into a very large number of triangles, and Kepler had
this device in mind. He found that the sums of suc-
cessive distances from his 360 points were approximately
proportional to the times from point to point, and was
thus enabled to represent much more accurately the
annual motion of the earth which produced the second
inequality of Mars, to whose motion he now returned.
Three points are sufficient to define a circle, so he took
three observed positions of Mars and found a circle ; he
then took three other positions, but obtained a different
circle, and a third set gave yet another. It thus began
to appear that the orbit could not be a circle. He next
tried to divide into 360 equal parts, as he had in the case
of the earth, but the sums of distances failed to fit the
times, and he realised that the sums of distances were
not a good measure of the area of successive triangles.
He noted, however, that the errors at the apses were now

KEPLER'S LAWS 41

smaller than with a central circular orbit, and of the
opposite sign, so he determined to try whether an oval
orbit would fit better, following a suggestion made by
Purbach in the case of Mercury, whose orbit is even
more eccentric than that of Mars, though observations
were too scanty to form the foundation of any theory.
Kepler gave his fancy play in the choice of an oval,
greater at one end than the other, endeavouring to satisfy
some ideas about epicyclic motion, but could not find a
satisfactory curve. He then had the fortunate idea of
trying an ellipse with the same axis as his tentative oval.
Mars now appeared too slow at the apses instead of too
quick, so obviously some intermediate ellipse must be
sought between the trial ellipse and the circle on the
same axis. At this point the " long arm of coincidence "
came into play. Half-way between the apses lay the
mean distance, and at this position the error was half
the distance between the ellipse and the circle, amount-
ing to '00429 of a radius. With these figures in his
mind, Kepler looked up the greatest optical inequality
of Mars, the angle between the straight lines from
Mars to the Sun and to the centre of the circle.1 The
secant of this angle was I -00429, so that he noted that
an ellipse reduced from the circle in the ratio of I -00429
to I would fit the motion of Mars at the mean distance
as well as the apses.

It is often said that a coincidence like this only happens
to somebody who "deserves his luck," but this simply
means that recognition is essential to the coincidence.
In the same way the appearance of one of a large number
of people mentioned is hailed as a case of the old adage
"Talk of the devil, etc.," ignoring all the people who
failed to appear. No one, however, will consider Kepler

is clearly a maximum at AMC in Fig. 2, when its tangent
= the eccentricity.

42 KEPLER

unduly favoured. His genius, in his case certainly "an
infinite capacity for taking pains," enabled him out of
his medley of hypotheses, mainly unsound, by dint of
enormous labour and patience, to arrive thus at the first
two of the laws which established his title of " Legislator
of the Heavens ".

FIGURES EXPLANATORY OF KEPLER'S
THEORY OF THE MOTION OF MARS.

FIG. i.

FIG. 2.

FlG. I. — In Ptolemy's excentric theory, A may be
taken to represent the earth, C the centre of a planet's
orbit, and E the equant, P (perigee) and Q (apogee)
being the apses of the orbit. Ptolemy's idea was that
uniform motion in a circle must be provided, and since
the motion was not uniform about the earth, A could not
coincide with C ; and since the motion still failed to be
uniform about A or C, some point E must be found
about which the motion should be uniform.

FlG. 2. — This is not drawn to scale, but is intended to
illustrate Kepler's modification of Ptolemy's excentric.
Kepler found velocities at P and Q proportional not to
AP and AQ but to AQ and AP, or to EP and EQ if
EC = CA (bisection of the excentricity). The velocity
at M was wrong, and AM appeared too great. Kepler's
first ellipse had M moved too near C. The distance
AC is much exaggerated in the figure, as also is MN.
AN = CP, the radius of the circle. MN should be

KEPLER'S LAWS 43

MC

•00429 of the radius, and -r~r should be 1-00429. The

velocity at N appeared to be proportional to EN( = AN).
Kepler concluded that Mars moved round PNQ, so that
the area described about A (the sun) was equal in equal
times, A being the focus of the ellipse PNQ. The
angular velocity is not quite constant about E, the
equant or empty focus, but the difference could hardly
have been detected in Kepler's time.

Kepler's improved determination of the earth's orbit
was obtained by plotting the different positions of the
earth corresponding to successive rotations of Mars, i.e.
intervals of 687 days. At each of these the date of the
year would give the angle MSE (Mars-Sun-Earth), and
Tycho's observation the angle MES. So the triangle
could be solved except for scale, and the ratio of SE to
SM would give the distance of Mars from the sun in
terms of that of the earth. Measuring from a fixed
position of Mars (e.g. perihelion), this gave the variation
of SE, showing the earth's inequality. Measuring from
a fixed position of the earth, it would give similarly a
series of positions of Mars, which, though lying not far
from the circle whose diameter was the axis of Mars'
orbit, joining perihelion and aphelion, always fell inside
the circle except at those two points. It was a long
time before it dawned upon Kepler that the simplest
figure falling within the circle except at the two extremi-
ties of the diameter, was an ellipse, and it is not clear
why his first attempt with an ellipse should have been
just as much too narrow as the circle was too wide.
The fact remains that he recognised suddenly that
halving this error was tantamount to reducing the circle
to the ellipse whose eccentricity was that of the old
theory, i.e. that in which the sun would be in one focus
and the equant in the other.

Having now fitted the ends of both major and minor

44 KEPLER

axes of the ellipse, he leaped to the conclusion that the
orbit would fit everywhere.

The practical effect of his clearing of the " second in-
equality " was to refer the orbit of Mars directly to the sun,
and he found that the area between successive distances of
Mars from the sun (instead of the sum of the distances)
was strictly proportional to the time taken, in short, equal
areas were described in equal times (2nd Law) when re-
ferred to the sun in the focus of the ellipse (ist Law).

He announced that (i) The planet describes an ellipse,
the sun being in one focus ; and (2) The straight line join-
ing the planet to the sun sweeps out equal areas in any two
equal intervals of time. These are Kepler's first and second
Laws though not discovered in that order, and it was at
once clear that Ptolemy's "bisection of the excentricity "
simply amounted to the fact that the centre of an ellipse
bisects the distance between the foci, the sun being in
one focus and the angular velocity being uniform about
the empty focus. For so many centuries had the fetish
of circular motion postponed discovery. It was natural
that Kepler should assume that his laws would apply
equally to all the planets, but the proof of this, as well
as the reason underlying the laws, was only given by
Newton, who approached the subject from a totally
different standpoint.

This commentary on Mars was published in 1609, the
year of the invention of the telescope, and Kepler
petitioned the Emperor for further funds to enable him
to complete the study of the other planets, but once more
there was delay; in 1612 Rudolph died, and his brother
Matthias who succeeded him, cared very little for as-
tronomy or even astrology, though Kepler was reappointed
to his post of Imperial Mathematician. He left Prague
to take up a permanent professorship at the University
of Linz. His own account of the circumstances is
gloomy enough. He says, " In the first place I could get

KEPLER'S LAWS 45

no money from the Court, and my wife, who had for a
long time been suffering from low spirits and despondency,
was taken violently ill towards the end of 1610, with the
Hungarian fever, epilepsy and phrenitis. She was
scarcely convalescent when all my three children were at
once attacked with smallpox. Leopold with his army
occupied the town beyond the river just as I lost the
dearest of my sons, him whose nativity you will find in
my book on the new star. The town on this side of the
river where I lived was harassed by the Bohemian troops,
whose new levies were insubordinate and insolent ; to com-
plete the whole, the Austrian army brought the plague
with them into the city. I went into Austria and en-
deavoured to procure the situation which I now hold.
Returning in June, I found my wife in a decline from her
grief at the death of her son, and on the eve of an in-
fectious fever, and I lost her also within eleven days of
my return. Then came fresh annoyance, of course, and
her fortune was to be divided with my step-sisters. The
Emperor Rudolph would not agree to my departure ;
vain hopes were given me of being paid from Saxony ;
my time and money were wasted together, till on the
death of the Emperor in 1612, I was named again by his
successor, and suffered to depart to Linz."

Being thus left a widower with a ten-year-old daughter
Susanna, and a boy Louis of half her age, he looked for
a second wife to take charge of them. He has given an
account of eleven ladies whose suitability he considered.
The first, an intimate friend of his first wife, ultimately
declined ; one was too old, another an invalid, another
too proud of her birth and quarterings, another could do
nothing useful, and so on. Number eight kept him
guessing for three months, until he tired of her constant
indecision, and confided his disappointment to number
nine, who was not impressed. Number ten, introduced
by a friend, Kepler found exceedingly ugly and enor-

46 KEPLER

mously fat, and number eleven apparently too young.
Kepler then reconsidered one of the earlier ones, dis-
regarding the advice of his friends who objected to her
lowly station. She was the orphan daughter of a cabinet-
maker, educated for twelve years by favour of the Lady
of Stahrenburg, and Kepler writes of her : " Her person
and manners are suitable to mine ; no pride, no extra-
vagance ; she can bear to work ; she has a tolerable
knowledge of how to manage a family ; middle-aged and
of a disposition and capability to acquire what she still
wants ".

Wine from the Austrian vineyards was plentiful and
cheap at the time of the marriage, and Kepler bought a
few casks for his household. When the seller came to
ascertain the quantity, Kepler noticed that no proper
allowance was made for the bulging parts, and the upshot
of his objections was that he wrote a book on a new
method of gauging — one of the earliest specimens of
modern analysis, extending the properties of plane figures
to segments of cones and cylinders as being "incorporated
circles". He was summoned before the Diet at Ratis-
bon to give his opinion on the Gregorian Reform of the
Calendar, and soon afterwards was excommunicated,
having fallen foul of the Roman Catholic party at Linz
just as he had previously at Gratz, the reason apparently
being that he desired to think for himself. Meanwhile
his salary was not paid any more regularly than before,
and he was forced to supplement it by publishing what
he called a " vile prophesying almanac which is scarcely
more respectable than begging unless it be because it
saves the Emperor's credit, who abandons me entirely,
and with all his frequent and recent orders in council,
would suffer me to perish with hunger ".

In 1617 he was invited to Italy to succeed Magini as
Professor of Mathematics at Bologna. Galileo urged
him to accept the post, but he excused himself on the

KEPLER'S LAWS 47

ground that he was a German and brought up among
Germans with such liberty of speech as he thought might
get him into trouble in Italy. In 1619 Matthias died
and was succeeded by Ferdinand III, who again retained
Kepler in his post. In the same year Kepler reprinted
his " Mysterium Cosmographicum," and also published
his " Harmonics " in five books dedicated to James I of
England. "The first geometrical, on the origin and
demonstration of the laws of the figures which produce
harmonious proportions; the second, architectonical, on
figurate geometry and the congruence of plane and solid
regular figures ; the third, properly Harmonic, on the
derivation of musical proportions from figures, and on
the nature and distinction of things relating to song, in
opposition to the old theories ; the fourth, metaphysical,
psychological, and astrological, on the mental essence of
Harmonics, and of their kinds in the world, especially on
the harmony of rays emanating on the earth from the
heavenly bodies, and on their effect in nature and on
the sublunary and human soul ; the fifth, astronomical
and metaphysical, on the very exquisite Harmonics of
the celestial motions and the origin of the excentricities
in harmonious proportions." The extravagance of his
fancies does not appear until the fourth book, in which
he reiterates the statement that he was forced to adopt
his astrological opinions from direct and positive obser-
vation. He despises "The common herd of prophesiers
who describe the operations of the stars as if they were
a sort of deities, the lords of heaven and earth, and
producing everything at their pleasure. They never
trouble themselves to consider what means the stars
have of working any effects among us on the earth
whilst they remain in the sky and send down nothing to
us which is obvious to the senses, except rays of light."
His own notion is "Like one who listens to a sweet
melodious song, and by the gladness of his countenance,

48 KEPLER

by his voice, and by the beating of his hand or foot
attuned to the music, gives token that he perceives and
approves the harmony : just so does sublunary nature,
with the notable and evident emotion of the bowels of
the earth, bear like witness to the same feelings, especially
at those times when the rays of the planets form
harmonious configurations on the earth," and again " The
earth is not an animal like a dog, ready at every nod ;
but more like a bull or an elephant, slow to become
angry, and so much the more furious when incensed."
He seems to have believed the earth to be actually a
living animal, as witness the following : " If anyone
who has climbed the peaks of the highest mountains,
throw a stone down their very deep clefts, a sound is
heard from them ; or if he throw it into one of the
mountain lakes, which beyond doubt are bottomless, a
storm will immediately arise, just as when you thrust a
straw into the ear or nose of a ticklish animal, it shakes
its head, or runs shudderingly away. What so like
breathing, especially of those fish who draw water into
their mouths and spout it out again through their gills,
as that wonderful tide ! For although it is so regulated
according to the course of the moon, that, in the preface
to my ' Commentaries on Mars/ I have mentioned it as
probable that the waters are attracted by the moon, as
iron by the loadstone, yet if anyone uphold that the earth
regulates its breathing according to the motion of the
sun and moon, as animals have daily and nightly
alternations of sleep and waking, I shall not think his
philosophy unworthy of being listened to ; especially if
any flexible parts should be discovered in the depths of
the earth, to supply the functions of lungs or gills."

In the same book Kepler enlarges again on his views
in reference to the basis of astrology as concerned with
nativities and the importance of planetary conjunctions.
He gives particulars of his own nativity. " Jupiter

KEPLER'S LAWS 49

nearest the nonagesimal had passed by four degrees the
trine of Saturn ; the Sun and Venus in conjunction were
moving from the latter towards the former, nearly in
sextiles with both : they were also removing from quadra-
tures with Mars, to which Mercury was closely approach-
ing : the moon drew near to the trine of the same planet,
close to the Bull's Eye even in latitude. The 25th
degree of Gemini was rising, and the 22nd of Aquarius
culminating. That there was this triple configuration on
that day — namely the sextile of Saturn and the Sun, the
sextile of Mars and Jupiter, and the quadrature of Mercury
and Mars, is proved by the change of weather ; for after
a frost of some days, that very day became warmer, there
was a thaw and a fall of rain." This alleged " proof" is
interesting as it relies on the same principle which was
held to justify the correction of an uncertain birth-time,
by reference to illnesses, etc., met with later. Kepler
however goes on to say, " If I am to speak of the results
of my studies, what, I pray, can I find in the sky, even
remotely alluding to it ? The learned confess that several
not despicable branches of philosophy have been newly
extricated or amended or brought to perfection by me :
but here my constellations were, not Mercury from the
East in the angle of the seventh, and in quadratures with
Mars, but Copernicus, but Tycho Brahe, without whose
books of observations everything now set by me in the
clearest light must have remained buried in darkness ;
not Saturn predominating Mercury, but my lords the
Emperors Rudolph and Matthias, not Capricorn the
house of Saturn but Upper Austria, the house of the
Emperor, and the ready and unexampled bounty of his
nobles to rriy petition. Here is that corner, not the
western one of the horoscope, but on the earth whither,
by permission of my Imperial master, I have betaken
myself from a too uneasy Court ; and whence, during these
years of my life, which now tends towards its setting,

4

50 KEPLER

emanate these Harmonics and the other matters on which
I am engaged."

The fifth book contains a great deal of nonsense about
the harmony of the spheres ; the notes contributed by
the several planets are gravely set down, that of Mercury
having the greatest resemblance to a melody, though
perhaps more reminiscent of a bugle-call. Yet the book
is not all worthless for it includes Kepler's Third Law,
which he had diligently sought for years. In his own
words, "The proportion existing between the periodic
times of any two planets is exactly the sesquiplicate
proportion of the mean distances of the orbits," or as
generally given, " the squares of the periodic times are
proportional to the cubes of the mean distances." Kepler
was evidently transported with delight and wrote, " What
I prophesied two and twenty years ago, as soon as I
discovered the five solids among the heavenly orbits, —
what I firmly believed long before I had seen Ptolemy's
'Harmonics' — what I had promised my friends in the
title of this book, which I named before I was sure of my
discovery, — what sixteen years ago I urged as a thing to
be sought, — that for which I joined Tycho Brahe, for
which I settled in Prague, for which I have devoted the
best part of my life to astronomical computations, at
length I have brought to light, and have recognised its
truth beyond my most sanguine expectations. Great as
is the absolute nature of Harmonics, with all its details
as set forth in my third book, it is all found among the
celestial motions, not indeed in the manner which I
imagined (that is not the least part of my delight), but
in another very different, and yet most perfect and
excellent. It is now eighteen months since I got the
first glimpse of light, three months since the dawn, very
few days since the unveiled sun, most admirable to gaze
on, burst out upon me. Nothing holds me; I will
indulge in my sacred fury ; I will triumph over mankind

KEPLER'S LAWS 51

by the honest confession that I have stolen the golden
vases of the Egyptians to build up a tabernacle for my
God far away from the confines of Egypt. If you forgive
me, I rejoice, if you are angry, I can bear it ; the die is
cast, the book is written ; to be read either now or by
posterity, I care not which ; it may well wait a century
for a reader, as God has waited six thousand years for
an observer." He gives the date i$th May, 1618, for
the completion of his discovery. In his "Epitome of
the Copernican Astronomy," he gives his own idea as to
the reason for this Third Law. " Four causes concur for
lengthening the periodic time. First, the length of the path ;
secondly, the weight or quantity of matter to be carried ;
thirdly, the degree of strength of the moving virtue;
fourthly, the bulk or space into which is spread out the
matter to be moved. The orbital paths of the planets
are in the simple ratio of the distances ; the weights or
quantities of matter in different planets are in the sub-
duplicate ratio of the same distances, as has been already
proved ; so that with every increase of distance a planet
has more matter and therefore is moved more slowly,
and accumulates more time in its revolution, requiring
already, as it did, more time by reason of the length of
the way. The third and fourth causes compensate each
other in a comparison of different planets; the simple
and subduplicate proportion compound the sesquiplicate
proportion, which therefore is the ratio of the periodic
times." The only part of this "explanation" that is true
is that the paths are in the simple ratio of the distances,
the "proof" so confidently claimed being of the circular
kind commonly known as " begging the question ". It
was reserved for Newton to establish the Laws of Motion,
to find the law of force that would constrain a planet to
obey Kepler's first and second Laws, and to prove that it
must therefore also obey the third.

CHAPTER VI.

CLOSING YEARS.

SOON after its publication Kepler's " Epitome " was placed
along with the book of Copernicus, on the list of books
prohibited by the Congregation of the Index at Rome,
and he feared that this might prevent the publication or
sale of his books in Austria also, but was told that though
Galileo's violence was getting him into trouble, there would
be no difficulty in obtaining permission for learned men
to read any prohibited books, and that he (Kepler) need
fear nothing so long as he remained quiet.

In his various works on Comets, he adhered to the
opinion that they travelled in straight lines with varying
velocity. He suggested that comets come from the re-
motest parts of ether, as whales and monsters from the
depth of the sea, and that perhaps they are something
of the nature of silkworms, and are wasted and con-
sumed in spinning their own tails. Napier's invention of
logarithms at once attracted Kepler's attention. He must
have regretted that the discovery was not made early
enough to save him a vast amount of labour in computa-
tions, but he managed to find time to compute some
logarithm tables for himself, though he does not seem to
have understood quite what Napier had done, and though
with his usual honesty he gave full credit to the Scottish
baron for his invention.

Though Eugenists may find a difficulty in reconciling
Napier's brilliancy with the extreme youth of his parents,

CLOSING YEARS 53

they may at any rate attribute Kepler's occasional fits of
bad temper to heredity. His cantankerous mother,
Catherine Kepler, had for some years been carrying on
an action for slander against a woman who had accused
her of administering a poisonous potion. Dame Kepler
employed a young advocate who for reasons of his own
" nursed " the case so long that after five years had elapsed
without any conclusion being reached another judge was
appointed, who had himself suffered from the caustic
tongue of the prosecutrix, and so was already prejudiced
against her. The defendant, knowing this, turned the
tables on her opponent by bringing an accusation of
witchcraft against her, and Catherine Kepler was im-
prisoned and condemned to the torture in July, 1620.
Kepler, hearing of the sentence, hurried back from Linz,
and succeeded in stopping the completion of the sentence,
securing his mother's release the following year, as it
was made clear that the only support for the case against
her was her own intemperate language. Kepler returned
to Linz, and his mother at once brought another action
for costs and damages against her late opponent, but died
before the case could be tried.

A few months before this Sir Henry Wotton, English
Ambassador to Venice, visited Kepler, and finding him
as usual, almost penniless, urged him to go to England,
promising him a warm welcome there. Kepler, however,
would not at that time leave Germany, giving several
reasons, one of which was that he dreaded the confinement
of an island. Later on he expressed his willingness to
go as soon as his Rudolphine Tables were published, and
lecture on them, even in England, if he could not do it
in Germany, and if a good enough salary were forthcoming.

In 1624 he went to Vienna, and managed to extract
from the Treasury 6000 florins on account of expenses
connected with the Tables, but, instead of a further grant,
was given letters to the States of Swabia, which owed

54 KEPLER

money to the Imperial treasury. Some of this he suc-
ceeded in collecting, but the Tables were still further
delayed by the religious disturbances then becoming
violent. The Jesuits contrived to have Kepler's library
sealed up, and, but for the Imperial protection, would
have imprisoned him also; moreover the peasants re-
volted and blockaded Linz. In 1627, however, the long
promised Tables, the first to discard the conventional
circular motion, were at last published at Ulm in four
parts. Two of these parts consisted of subsidiary Tables,
of logarithms and other computing devices, another con-
tained Tables of the elements of the sun, moon, and
planets, and the fourth gave the places of a thousand
stars as determined by Tycho, with Tycho's refraction
Tables, which had the peculiarity of using different values
for the refraction of the sun, moon, and stars. From a
map prefixed to some copies of the Tables, we may infer
that Kepler was one of the first, if not actually the first,
to suggest the method of determining differences of longi-
tude by occultations of stars at the moon's limb. In an
Appendix, he showed how his Tables could be used by
astrologers for their predictions, saying " Astronomy is
the daughter of Astrology, and this modern Astrology
again is the daughter of Astronomy, bearing something
of the lineaments of her grandmother ; and, as I have
already said, this foolish daughter, Astrology, supports
her wise but needy mother, Astronomy, from the profits
of a profession not generally considered creditable ".
There is no doubt that Kepler strongly resented having
to depend so much for his income on such methods which
he certainly did not consider creditable.

It was probably Galileo whose praise of the new Tables
induced the Grand Duke of Tuscany to send Kepler a
gold chain soon after their publication, and we may
perhaps regard it as a mark of favour from the Emperor
Ferdinand that helper mitted1 Kepler to attach himself to

CLOSING YEARS 55

the great Wallenstein, now Duke of Friedland, and a firm
believer in Astrology. The Duke was a better paymaster
than either of the three successive Emperors. H e furnished
Kepler with an assistant and a printing press ; and ob-
tained for him the Professorship of Astronomy at the
University of Rostock in Mecklenburg. Apparently,
however, the Emperor could not induce Wallenstein to
take over the responsibility of the 8000 crowns, still owing
from the Imperial treasury on account of the Rudolphine
Tables. Kepler made a last attempt to secure payment
at Ratisbon, but his journey thither brought disappoint-
ment and fatigue and left him in such a condition that he
rapidly succumbed to an attack of fever, dying in Novem-
ber, 1630, in his fifty-ninth year. His body was buried at
Ratisbon, but the tombstone was destroyed during the
war then raging. His daughter, Susanna, the wife of
Jacob Bartsch, a physician who had helped Kepler with
his Ephemeris, lost her husband soon after her father's
death, and succeeded in obtaining part of Kepler's arrears
of salary by threatening to keep Tycho's manuscripts,
but her stepmother was left almost penniless with
five young children. For their benefit Louis Kepler
printed a " Dream of Lunar Astronomy," which first
his father and then his brother-in-law had been preparing
for publication at the time of their respective deaths. It
is a curious mixture of saga and fairy tale with a little
science in the way of astronomy studied from the moon,
and cast in the form of a dream to overcome the practical
difficulties of the hypothesis of visiting the moon. Other
writings in large numbers were left unpublished. No
attempt at a complete edition of Kepler's works was
made for a long time. One was projected in 1714 by
his biographer, Hantsch, but all that appeared was one
volume of letters. After various learned bodies had
declined to move in the matter the manuscripts were
purchased for the Imperial Russian library. An edition

56 KEPLER

was at length brought out at Frankfort by C. Frisch, in
eight volumes, appearing at intervals from 1858-1870.

Kepler's fame does not rest upon his voluminous works.
With his peculiar method of approaching problems there
was bound to be an inordinate amount of chaff mixed
with the grain, and he used no winnowing machine.
His simplicity and transparent honesty induced him to
include everything, in fact he seemed to glory in the
number of false trails he laboriously followed. He was
one who might be expected to find the proverbial " needle
in a haystack," but unfortunately the needle was not
always there. Delambre says, "Ardent, restless, burning
to distinguish himself by his discoveries he attempted
everything, and having once obtained a glimpse of one,
no labour was too hard for him in following or verify-
ing it. All his attempts had not the same success, and
in fact that was impossible. Those which have failed
seem to us only fanciful ; those which have been more
fortunate appear sublime. When in search of that which
really existed, he has sometimes found it ; when he devoted
himself to the pursuit of a chimera, he could not but fail,
but even then he unfolded the same qualities, and that
obstinate perseverance that must triumph ove^r all diffi-
culties but those which are insurmountable." Berry, in
his "Short History of Astronomy," says "as one reads
chapter after chapter without a lucid, still less a correct
idea, it is impossible to refrain from regrets that the in-
telligence of Kepler should have been so wasted, and it is
difficult not to suspect at times that some of the valuable
results which lie embedded in this great mass of tedious
speculation were arrived at by a mere accident. On the
other hand it must not be forgotten that such accidents
have a habit of happening only to great men, and that if
Kepler loved to give reins to his imagination he was
equally impressed with the necessity of scrupulously com-
paring speculative results with observed facts, and of

CLOSING YEARS 57

surrendering without demur the most beloved of his
fancies if it was unable to stand this test. If Kepler had
burnt three-quarters of what he printed, we should in all
probability have formed a higher opinion of his intellectual
grasp and sobriety of judgment, but we should have lost
to a great extent the impression of extraordinary en-
thusiasm and industry, and of almost unequalled intel-
lectual honesty which we now get from a study of his
works. "

Professor Forbes is more enthusiastic. In his " History
of Astronomy," he refers to Kepler as " the man whose
place, as is generally agreed, would have been the most
difficult to fill among all those who have contributed
to the advance of astronomical knowledge," and again
a propos of Kepler's great book, " it must be obvious that
he had at that time some inkling of the meaning of his
laws — universal gravitation. From that moment the
idea of universal gravitation was in the air, and hints and
guesses were thrown out by many ; and in time the law
of gravitation would doubtless have been discovered,
though probably not by the work of one man, even if
Newton had not lived. But, if Kepler had not lived, who
else could have discovered his Laws ? "

APPENDIX I.

LIST OF DATES.

JOHANN KEPLER, born 1571 ; school at Maulbronn, 1586; Uni-
versity of Tubingen, 1589; M.A. of Tubingen, 1591 ; Professor
at Gratz, 1594; "Prodromus," with " Mysterium Cosmo-
graphicum," published 1596; first marriage, 1597; joins
Tycho Brahe at Prague, 1600 ; death of Tycho, 1601 ; Kepler's
optics, 1603 ; Nova, 1604 ; on Comets, 1607 ; Commentary on
Mars, including First and Second Laws, 1609; Professor at
Linz, 1612; second marriage, 1613; Third Law discovered,
1618 ; Epitome of Copernican Astronomy, 1618-1621 ;
Rudolphine Tables published, 1627 ; died, 1630.

(59)

APPENDIX II.

BIBLIOGRAPHY.

FOR a full account of the various systems of Kepler and his
predecessors the reader cannot do better than consult the
"History of the Planetary Systems, from Thales to Kepler,"
by Dr. J. L. E. Dreyer (Cambridge Univ. Press, 1906). The
same author's " Tycho Brahe " gives a wealth of detail about
that "Phoenix of Astronomers," as Kepler styles him. A
great proportion of the literature relating to Kepler is Ger-
man, but he has his place in the histories of astronomy, from
Delambre and the more modern R. Wolfs " Geschichte" to
those of A. Berry, " History of Astronomy " (University Ex-
tension Manuals, Murray, 1898), and Professor G. Forbes,
"History of Astronomy" (History of Science Series, Watts,
1909).

(60)

GLOSSARY.

Apogee : The point in the orbit of a celestial body when it is furthest
from the earth.

Apse : An extremity of the major axis of the orbit of a body ; a
body is at its greatest and least distances from the body
about which it revolves, when at one or other apse.

Conjunction : When a plane containing the earth's axis and passing
through the centre of the sun also passes through that of the
moon or a planet, at the same side of the earth, the moon or
planet is in conjunction, or if on opposite sides of the earth,
the moon or planet is in opposition. Mercury and Venus
cannot be in opposition, but are in inferior or superior con-
junction according as they are nearer or further than the sun.

Deferent : In the epicyclic theory, uneven motion is represented by
motion round a circle whose centre travels round another
circle, the latter is called the deferent.

Ecliptic : The plane of the earth's orbital motion about the sun,
which cuts the heavens in a great circle. It is so called
because obviously eclipses can only occur when the moon is
also approximately in this plane, besides being in conjunction
or opposition with the sun.

Epicycle : A point moving on the circumference of a circle whose
centre describes another circle, traces an epicycle with
reference to the centre of the second circle.

Equant : In Ptolemy's excentric theory, when a planet is describing
a circle about a centre which is not the earth, in order to
satisfy the convention that the motion must be uniform, a
point was found about which the motion was apparently
uniform,1 and this point was called the equant.

Equinox : When the sun is in the plane of the earth's equator
the lengths of day and night are equal. This happens twice
a year, and the times when the sun passes the equator are
called the vernal or spring equinox and the autumnal equinox
respectively.

1 I.e. the angular motion about the equant was uniform.
(61)

62 KEPLER

Ejection: The second inequality of the moon, which vanishes at
new and full moon and is a maximum at first and last
quarter.

Excentric : As an alternative to epicycles, planets whose motion
round the earth was not uniform could be represented as
moving round a point some distance from the earth called
the excentric.

Geocentric : Referred to the centre of the earth ; e.g. Ptolemy's
theory.

Heliocentric: Referred to the centre of the sun; e.g. the theory
commonly called Copernican.

Inequality : The difference between the actual position of a planet
and its theoretical position on the hypothesis of uniform
circular motion.

Node : The points where the orbit of the moon or a planet intersect
the plane of the ecliptic. The ascending node is the one
when the planet is moving northwards, and the line of inter-
section of the orbital plane with the ecliptic is the line of
nodes.

Occultation : Usually means when a planet or star is hidden by the
moon, but it also includes " occultation " of a star by a planet
or of a satellite by a planet or of one planet by another.

Opposition v. Conjunction.

Parallax: The error introduced by observing from some point
other than that required in theory, e.g. in geocentric places
because the observations are made from the surface of the
earth instead of the centre, or in heliocentric places be-
cause observations are made from the earth and not from
the sun.

Perigee: The point in the orbit of a celestial body when it is
nearest to the earth.

Precession : Owing to the slow motion of the earth's pole around
the pole of the ecliptic, the equator cuts the ecliptic a little
earlier every year, so that the equinox each year slightly
precedes, with reference to the stars, that of the previous
year.

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